Analyses of isotropic elastic properties of graphite particles contained in ductile cast iron

A recent article by Andriollo and Hattel (2016) from the Department of Mechanical Engineering, at Technical University of Denmark and published in Mechanics of Materials aimed at determining an effective elastic constitutive description of graphite nodules contained in ductile cast iron based on physical grounds, to be used for further investigation of the material mechanical behavior at the micro-scale.

Ductile cast iron, also known as spheroidal graphite iron is commonly applied in automotive and wind power industry due to its castability, high ductility and strength combined with relatively low manufacturing cost. Spheroidal graphite iron properties are controlled by chemical composition, cooling rate and heat treatment. The final material microstructure may be naturally considered as composite (Grimvall, G., Adv. Mater. Res, 1997) consisting of graphite particles, called nodules, embedded in a continuous matrix which in most engineering applications can be ferritic, pearlitic or both. While the mechanical properties of the matrix are quite well-established, a comprehensive quantitative description of the elastic behavior of the nodules is still missing in the published literature.

In some micro-mechanical analyses, the graphite nodules are simply regarded as voids due to their presumed negligible stiffness and weak bonding with the surrounding matrix. However, this assumption is controversial, as it is based on microscopy observations of early debonding for nodules sitting on the surface of tensile test specimens, where the stress state is substantially biaxial. According to Liu et al. (Mater. Lett, 2002.), the stress state around nodules located in bulk is likely to be different, due to the intrinsic material inhomogeneity; therefore it seems not possible to conclude that interface debonding always occurs independently of the real local loading conditions.

In addition, there are indications suggesting a non-negligible influence of the graphite nodules on the spheroidal graphite iron mechanical response. Firstly, low-cycle fatigue behavior is better reproduced by numerical models where the nodules are treated as rigid spheres instead of voids. Secondly, tensile stress-strain curves for spheroidal graphite iron are never linear even at very low stress levels, and cannot be justified with a simple “voided matrix” model. Thirdly, during compression tests performed at high temperature the nodules do not deform at all, whereas the surrounding matrix undergoes extensive plastic deformation. Due to these facts, it is clear that a thorough and complete understanding of spheroidal graphite iron mechanical behavior can only be achieved if accurate information on the nodules’ constitutive properties is available.

Nevertheless, the only quantitative information concerning their elastic properties comes from nano-indentation tests performed according to Oliver-Pharr method (Oliver and Pharr, 1992, J. Mater. Res.), whose reliability is somewhat disputable because a priori values for Poisson’s ratio must be assumed and moreover the graphite nodules are not isotropic at nanoscale, meaning that the concept of indentation-based Young’s modulus loses its significance.

The lack of reliable knowledge concerning the nodules’ mechanical behavior motivates the analysis presented in this article, which rests on the following assumptions: 1) the graphite nodules can be considered as mechanically isotropic, 2) their behavior can be described by a linear elastic model and 3) their basic building blocks are graphite platelets with hexagonal structures.

Initially, the authors show that application of elastic bound-theory analysis for hexagonal polycrystals leads to the definition of an admissible domain for the nodules’ elastic constants. After that, values from the domain are used to simulate the mechanical behavior of spheroidal graphite iron at the macro-scale using a 3D unit cell model implemented in commercial finite element software. Remarkably, it is found that values for the nodules’ Young’s modulus and Poisson’s ratio belonging to the admissible domain never allow recovering the experimentally observed response of common ferritic grades of ductile cast iron. Furthermore, this important conclusion still holds when the influence of three relevant phenomena is taken into account: weak interface bonding between the nodules and the matrix, local microscopic residual stresses arising during solid state cooling and inelastic deformation of the nodules.

On the basis of the aforementioned results, the authors conclude that the graphite nodules contained in ductile cast iron may not be considered as isotropic at the microscopic scale, at least from a mechanical standpoint. Hence, a satisfactory elastic constitutive description should take into consideration their intrinsic inhomogeneity and anisotropy.